For the brain to function correctly, its neurons must be connected correctly. Axons often have to grow over long distances to find appropriate targets. Some of the most important guidance cues they use to achieve this feat are gradients of increasing concentration of guidance molecules. The mechanisms by which axons sense and respond to these gradients are largely unknown. Understanding these mechanisms is important for understanding how the brain normally develops. It is also crucial for understanding how neural connections regenerate, and designing effective therapies to enable axons to grow back to appropriate targets and thus restore lost function after injury. Previous work to uncover these mechanisms has been largely qualitative and based on extremely crude technologies. In this project we will develop a uniquely quantitative approach, based on a combination of mathematical modelling and sophisticated technologies borrowed from other domains. We will paint patterns of guidance molecules onto the surface of a collagen gel in which axons are growing and, using quantitative modelling of molecular diffusion, calculate the resulting gradients in the gel which the axons then encounter. By maintaining fine control over the pattern of molecules applied, we will achieve fine control over the parameters of the gradient. This will allow systematic variation of gradient parameters, and thus systematic investigation of the way each of these parameters regulates axon guidance. The principle rewards of developing this technology are that it will provide a unique tool for probing axon guidance mechanisms that will be useful to a wide range of researchers. It will push the field forward by providing a previously unavailable quantitative testbed for studying such issues as receptor-ligand interactions and pharmacological manipulations of gradient sensing processes. An ultimate goal is to speed up the discovery of ways to stimulate recovery from damage to the nervous system.